Add and simplify the expression: $ \frac{4}{k+1} + \frac{k}{k-5} $.

$ \frac{k^2+5k-20}{(k+1)(k-5)} $

$ \frac{k^2-k-20}{(k+1)(k-5)} $

Adding and Subtracting Rational Expressions Practice — Grade 9 math

Lesson 90: Adding and Subtracting Rational Expressions — Practice Questions

1. What is the result of subtracting $ \frac{x}{2} - \frac{z}{7} $?
- A. $ \frac{x-z}{-5} $
- B. $ \frac{x-z}{14} $
- C. $ \frac{7x-2z}{14} $
- D. $ \frac{2x-7z}{14} $
2. What is the least common denominator (LCD) for the expression $ \frac{3}{x+4} + \frac{x}{x^2 - 16} $?
- A. $ (x+4)(x^2 - 16) $
- B. $ (x-4)(x+4) $
- C. $ x^2 - 16 $
- D. $ x+4 $
3. Subtract and simplify the expression completely: $ \frac{4x}{x^2 - 4} - \frac{2}{x - 2} $. The simplified form is ___.
4. Subtract and simplify: $ \frac{c+1}{c-2} - \frac{5}{c^2+c-6} $. The result is ___.
5. Add and simplify the expression: $ \frac{4}{k+1} + \frac{k}{k-5} $.
- A. $ \frac{k+4}{2k-4} $
- B. $ \frac{k^2+5k-20}{(k+1)(k-5)} $
- C. $ \frac{k^2-k-20}{(k+1)(k-5)} $
- D. $ \frac{4k-20+k^2}{k-5} $
6. Subtract and simplify the expression to a single number: $$\frac{6x + 1}{x - 2} - \frac{2x + 9}{x - 2}$$ The simplified result is ___.
7. Add and simplify the expression: $$\frac{2k}{k + 7} + \frac{14}{k + 7}$$
- A. 2
- B. $\frac{2k + 14}{2k + 14}$
- C. $\frac{2(k+7)}{k+7}$
- D. $\frac{2k+14}{(k+7)^2}$
8. Which expression is the result of subtracting and simplifying $$\frac{7x + 4}{x - 3} - \frac{3x - 8}{x - 3}$$?
- A. $\frac{4x + 12}{x - 3}$
- B. $\frac{4x - 4}{x - 3}$
- C. 4
- D. $\frac{10x - 4}{x - 3}$
9. Add and simplify completely: $$\frac{3a^3}{20a} + \frac{7a^3}{20a}$$ The simplified expression is ___.
10. When subtracting $$\frac{c - 9}{c + 2}$$ from $$\frac{5c + 1}{c + 2}$$, what is the correct numerator after combining the fractions but before simplifying?
- A. (5c + 1) - (c - 9)
- B. 5c + 1 - c - 9
- C. (5c + 1) + (c - 9)
- D. 4c + 10